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1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.
11

%I #30 Jun 09 2018 06:16:59

%S 2,3,3,4,3,5,3,5,4,6,3,6,3,6,4,6,3,7,3,7,5,7,3,7,4,7,5,7,3,8,3,7,4,8,

%T 4,8,3,8,5,8,3,9,3,8,6,8,3,8,4,9,4,8,3,9,5,8,6,9,3,9,3,8,6,8,4,9,3,9,

%U 5,9,3,9,3,9,5,9,4,10,3,9,6,10,3,10,6,9,4,9,3,10,4,9,5,9,4,9,3,9,6,10,3,10

%N 1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.

%C Analogous sequences of iteration-lengths for A000005 or A000010 are A036459 and A049108 resp. The length values of 3 occur if the initial value is prime resulting in {p,1,0} iterations.

%H T. D. Noe, <a href="/A053475/b053475.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A076640(n) + 1. - _Michael De Vlieger_, Jul 04 2016

%e Starting with n=18, the iterations of A051953 are as follows: {18,12,8,4,2,1,0}. The length of this sequence is 7, so a(18) = 7. The function is applied a(n)-1 times.

%t Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &], {n, 84}] (* _Michael De Vlieger_, Jul 04 2016 *)

%Y Cf. A000005, A000010, A051953, A036459, A049108, A076640.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 14 2000